"The worst part is the bathrooms," passenger Donna Gutzman told NBC News. "There's no water. You can't really flush so everyone's going in little plastic baggies and putting it outside their rooms."

Fewer than two dozen public toilets are working, Carnival said.

The ship is being towed to port in Mobile, Ala., and is expected to arrive some time Thursday. A weekend fire left the vessel disabled without propulsion and stranded at sea.

Lindsey Peterson, whose parents are onboard the Triumph, said she's hearing conflicting reports. "Carnival is telling me that all the passengers are safe, the boat has 40 percent power, they have one dining room working with hot food and hot coffee, that the sleeping conditions are fine," Peterson said. "Everything that Carnival has told me thus far has not matched up with what my mom has said."

Tess Hester, whose daughter is on the ship, received this message: "This is honestly the worst experience ever. I'm not sure I can take two more days at sea with no food, water or power."

One of the biggest concerns crew members will have until the ship docks is the potential for disease outbreak, particularly norovirus, which causes vomiting and diarrhea, Jay Herring, a former senior officer for Carnival Cruise Lines, told The Associated Press.

"Housekeeping, others are probably working double shifts to keep the mess clean and wipe down and sanitize all the common areas," said Herring, who worked for Carnival from 2002 to 2004 and spent four months on the Triumph.

Carnival apologizes
"I think it's very important that I apologize to our guests and to their families that have been affected by this very difficult situation," Carnival CEO Gerry Cahill said. The cruise line has reserved 1,500 hotel rooms for passengers in Mobile and New Orleans, and 20 chartered flights will transport passengers to Houston, Cahill said at a press conference on Tuesday.

The Coast Guard and the National Transportation Safety Board are investigating the cause of the engine-room fire. The fire broke out Sunday morning as the Triumph -- with 3,143 passengers and 1,086 crew members on board -- was sailing about 150 miles off the coast of the Yucatan Peninsula. The flames were put out without any injuries to passengers or crew.

The disabled ship was originally going to be towed to the Mexican port of Progreso, but strong winds pushed them 90 miles north. Carnival decided to tow the ship to Mobile instead, making it easier for passengers traveling with passports to get home.

The ship left Galveston, Texas, on Thursday, and was scheduled to return on Monday. Passengers will receive a full refund and a future cruise credit, Carnival said.

The ship's next two voyages, scheduled to depart Monday and Saturday, have been canceled. Passengers scheduled to sail on either of those voyages will receive a full refund and a discount on a future cruise.

The incident comes more than two years after another Carnival ship, the Splendor, was crippled at seaby a fire in the engine room.